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Quadrilaterals

Quadrilaterals. Sara Beberman Olivia DeFlumeri Olivia Huynh Amanda Okaka. Parallelogram. A parallelogram is a quadrilateral with both pairs of opposite sides parallel - if a quadrilateral has two pairs of opposite sides congruent then it is a parallelogram ex: (AB ≅DC)

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Quadrilaterals

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  1. Quadrilaterals Sara Beberman Olivia DeFlumeri Olivia Huynh Amanda Okaka

  2. Parallelogram A parallelogram is a quadrilateral with both pairs of opposite sides parallel - if a quadrilateral has two pairs of opposite sides congruent then it is a parallelogram ex: (AB≅DC) -if a quadrilateral has two pairs of opposite angles congruent then it is a parallelogram ex:(<DAB≅ <DCB) -if a quadrilateral has one pair of opposite sides congruent and parallel then it is a parallelogram ex: (AD≅BC and ADllBC) -if a quadrilateral has diagonals that bisect each other then it is a parallelogram ex: (AE≅EC and DE≅EB)

  3. Parallelogram Properties of a parallelogram: -opposite sides are congruent (AB≅DC) -opposite angles are congruent (<ADC≅<ABC) -consecutive angles are supplementary (<DAB + <ABC= 180°) -diagonals bisect each other (AC bisects BD)

  4. A KITE • PROPERTIES • Two sets of adjacent sides are congruent • One set of congruent angles opposite each other • Diagonals are perpendicular • The longer diagonal of the kite bisects the shorter diagonal D E B -A quadrilateral with two distinct pairs of congruent adjacent sides. C • AB≅AD, DC≅BC, (Two sets of congruent adjacent sides) • AE is perpendicular to DB • DE≅EB (The longer diagonal bisects the shorter diagonal) • <ADC≅<ABC (One set of angles congruent)

  5. Rhombus Rhombus: a parallelogram with a pair of congruent adjacent sides Properties: • Opposite sides are congruent and parallel • AB  BC  CD  DA AB // CD and BC // DA • Opposite angles are congruent ABC ADC andBAD BCD • Consecutive angles are supplementary BAD + ABC = 180andADC + DCB = 180 BAD + ADC = 180andABC + DCB =180 • Diagonals bisect each other BO  DO and AO  CO • Diagonals are perpendicular AOB = BOC = COD = DOA = 90 • The diagonals bisect the angles BAC DAC, ABD CBD, BCA DCA, andCDB ADB

  6. Trapezoid Trapezoid: A quadrilateral, which has only one set of opposite sides parallel Properties: • Exactly one pair of opposite sides is parallel BC//AD • Consecutive angles on different bases are supplementary DAB + ABC = 180 and ADC + BCD = 180

  7. Rectangle • Properties of a Rectangle • both pairs of opposite sides are congruent and parallel • diagonals are congruent • diagonals bisect one another • consecutive angles are supplementary • both pairs of opposite angles are congruent • has 4 right angles Definition – A rectangle is a parallelogram that has four right angles, 2 sets of opposite sides congruent, and congruent diagonals • Ex. • * AB is Congruent and Parallel to DC, AD is Congruent and Parallel to BC • * Diagonal X and Diagonal Y are Congruent and bisect one another • * <A + <D = 180˚, <B + <C = 180˚, <A + <B = 180˚, <D + <C = 180˚ • <A ≅<C, <B≅<D • <A, <B, <C, and <D are all right angles (each equal 90˚) A B X Y C D

  8. Square * Definition – A parallelogram with all right angles and all side lengths congruent • Properties of a Square: • All sides are congruent • Opposite sides are parallel • All angles are congruent (all right angles) • Consecutive angles are supplementary • Diagonals are congruent • Diagonals are perpendicular • Diagonals bisect one another • Diagonals bisect the angles A square is both a rectangle and a rhombus. • Ex. • AB is congruent to BC is congruent to CD is congruent to AD • AB is parallel to DC, AD is parallel to BC • <A, <B, <C, <D are all right angles (all congruent) • <ABC + <BCD = 180° • BD = AC • AC is perpendicular to BD • AC bisects BD, BD bisects AC • BD bisects <ABC and <ADC, AC bisects <BAD, <BCD

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